Chronology for 1980 to 1990

1982Mandelbrot publishes The fractal geometry of nature which develops his theory of fractal geometry more fully than his work of 1975.

1982Freedman proves that any closed 4-dimensional manifold which is homotopy equivalent to the 4-sphere must be the 4-sphere. This proves a further case of the higher dimensional Poincaré conjecture following Smale's work in 1961.

1983Donaldson publishes Self-dual connections and the topology of smooth 4-manifolds which leads to totally new ideas concerning the geometry of 4-manifolds.

1983Faltings proves the "Mordell conjecture". He makes a major contribution to Fermat's Last Theorem showing that for every n there are at most a finite number of coprime integers x, y, z satisfying xn + yn = zn. (See this History Topic.)

1984Witten publishes Supersymmetry and Morse theory containing ideas that have become of central importance in the study of differential geometry.

1986Margulis proves the "Oppenheim conjecture" on the values of indefinite irrational quadratic forms at integer points.

1987Zelmanov proves an important conjecture about when an infinite dimensional Lie algebra is nilpotent.

1988Langlands is the first recipient of the National Academy of Sciences Award in Mathematics. He receives it for "extraordinary vision that has brought the theory of group representations into a revolutionary new relationship with the theory of automorphic forms and number theory."